On calculating the normalization constants in queueing networks

Queueing networks of the product-form type are widely used as models in the analysis and design of computer and telecommunication systems. But for many systems (closed networks or others with population constraints), the product form solution involves a normalization constant, whose calculation is not trivial. Harrison (1985) obtained some closed form expression for normalization constants. The method was elaborated by Gordon (1990). We propose an alternative method to obtain the closed form formula for normalization constants. Our approach is based on the fact that calculation of these normalization constants involves convolution procedures. The approach is a straightforward application of Z-transform